A note on Hadamard roots of rational functions

A. J. Van Der Poorten

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Suppose F is a polynomial and Σh≥0 F(bh)Xh represents a rational function. If the bh all belong to a field finitely generated over Q, then it is a generalization of a conjecture of Pisot that there is a sequence (ch) with F(ch) = F(bh) for h = 0, 1, . . . so that also Σh≥0 chXh represents a rational function. We explain the context of this Hadamard root conjecture and make some suggestions that might lead to its proof, emphasizing the apparent difficulties that have to be overcome and the ideas that might be employed to that end.

Original languageEnglish
Pages (from-to)1183-1197
Number of pages15
JournalRocky Mountain Journal of Mathematics
Volume26
Issue number3
Publication statusPublished - Jun 1996

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